Car security alarms go off at a mean rate of 4.0 per hour in a large costco parking lot. find the probability that in an hour there will be (round your answers to 4 decimal places.) probability (a) no alarms .0183 correct (b) fewer than two alarms .0916 correct (c) more than seven alarms .0511 correct

In this problem we would you use the Poisson distribution:

The formula is: p(k) = Pr ( = k) = e^- λ λ^k/k!

Where k is equal to 0, 1, 2…

λ = to the mean, therefore it is 4.0

a.    k = 0

p(0) = e^-4 4^0/0! = 0.0183

b.    < 2

< 2, use the additivity probability

= e^-4 4^0/0! + e^-4 4^1/1! + e^-4 4^2/2!

= 0.0916

c.    > 7

Use the probability of complementary events

=1 - (P( =0) + P( =1) + P( =2) + P( = 3) + +P( =4) + P( =5) + P( =6) + P( =7)) = 0.0511

what is the approximate angle of acb if abc is 25cm and the length of segment bc is 15

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4